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Singularity patterns in a chemotaxis model

Herrero, Miguel A. and Velázquez, J.J. L. (1996) Singularity patterns in a chemotaxis model. Mathematische Annalen, 306 (1). pp. 583-623. ISSN 0025-5831

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Abstract

The authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time. Such a finite-time blow-up of solutions implies chemotactic collapse, namely, concentration of species to form sporae. The model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity, which has the form ut=Δu−χ(uv), 0=Δv+(u−1), on ΩR2, where Ω is an open disc with no-flux (homogeneous Neumann) boundary conditions. The initial conditions are continuous functions u(x,0)=u0(x)≥0, v(x,0)=v0(x)≥0 for xΩ. Under these conditions, the authors prove there exists a radially symmetric solution u(r,t) which blows up at r=0, t=T<∞. A specific description of such a solution is presented. The authors also discuss the strong similarity between the chemotactic model they study and the classical Stefan problem.


Item Type:Article
Uncontrolled Keywords:Blow-up; equations; radial solutions; chemotactic collapse
Subjects:Medical sciences > Biology > Biomathematics
Sciences > Mathematics > Differential equations
ID Code:17199
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Deposited On:26 Nov 2012 09:36
Last Modified:07 Feb 2014 09:43

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